The sound field for singularities in motion

Abstract

A general expression for the sound field of a point force in arbitrary motion is found. The expression reduces to the classical results for both uniform rectilinear motion and uniform circular motion of a point force. The solution shows that a fluctuating force in motion will have two components in its radiative sound field; the first an essentially dipole term due to the time rate of change of the force, and the second an essentially quadrupole term due to the acceleration of the system in which the force is acting. This second effect has not been explicitly recognized in previous work. Applications include the vortex noise in rotating systems and helicopter main rotor noise. An expression for the sound field of a point source in arbitrary motion is also determined. This expression does not reduce to the classical result for uniform motion, and it is concluded that the classical result does not take proper account of the momentum output associated with the source. The present result also shows that a constant velocity mass source moving in an accelerative manner will radiate sound. A practical example is the tip jet rotor. The sound field for a point acoustic stress in arbitrary motion is determined and the accelerative effects are shown to produce higher order poles than the quadrupole normally associated with the acoustic stress tensor. Some preliminary interpretation of this result is presented. In all three cases the effect of a volume distribution of acoustic sources may be found by integration, and in all cases the effect of the acceleration terms becomes greater as speed is increased.